For which of the following values does ax^2 + 2x + c =0 not

Question

For which of the following values does ax^2 + 2x + c =0 not have any real root?
A) ac>1
B) ac-1
E) it cannot be determined from the information given

I have an OA, so please provide your explanations!

Fig · Answer

(A) for me

All is relying the study of b^2 - 4*a*c.... Actually, for the special case of b being an even, we can shortten this analysis by using the reduiced determinant : (b/2)^2 - a*c. So, with b = 2, we have: (b/2)^2 - a*c = 1 - a*c If 1 - a*c < 0, there is no real root. Hence, a*c > 1.

Juaz · Answer

for non real roots: (2^2-4ac) <0> ac>1

kumarajeet06 · Answer

quadratic equation ax^2 +bx +c =0 doesn't have real root when b^2-4ac <0 for the equation in question, b =2 so 4 -4ac <0>4<4ac>ac>1

techjanson · Answer

4 - 4ac < 0 is condition for imaginary roots
or 1 - ac < 0
or 1 < ac

Hence A

ricokevin · Answer

Same explanation, same answer.

Using the quadratic formula root test.

nervousgmat · Answer

Thanks, guys for your replies!
I had no idea about the quadratic formula root test. Never studied this in my life! 

The OA is A!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

For which of the following values does ax^2 + 2x + c =0 not

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards